Triangular Pyramid Calculator

Calculate volume, surface area, and other properties of a triangular pyramid (tetrahedron)

← to Pyramid Calculator

Calculate Using:

Side a: Side b: Side c:

Pyramid Height (h):

Calculation Results

Enter triangular pyramid measurements to calculate all properties.

Triangular Pyramid Diagram

Triangular Pyramid Formulas

Key Properties

Base Area (B): Area of the triangular base
Height (h): Perpendicular distance from base to apex
Volume (V): Space contained within the pyramid
Lateral Area (L): Area of the three triangular faces
Surface Area (A): Total area including the base
Base Perimeter (P): Perimeter of the triangular base
Slant Height (l): Height of the triangular faces

Calculation Formulas

Base Area (B): B = ½ × b × h_Δ
Volume (V): V = ⅓ × B × h
Surface Area (A): A = B + L
Base Perimeter (P): P = a + b + c
Regular Tetrahedron Volume: V = (a³√2)/12
Regular Tetrahedron Surface Area: A = a²√3

Where: b = base length of triangle, h_Δ = height of base triangle, a, c = other two sides of base triangle, h = height of pyramid, l = slant height of lateral faces

Example Calculation

For a triangular pyramid with:

Base (b) = 6 units, Base height (h_Δ) = 4 units, Sides a = 5 units, c = 5 units, Pyramid height (h) = 8 units.

Calculations:

Base Area = ½ × 6 × 4 = 12 units²
Base Perimeter = 5 + 6 + 5 = 16 units
Volume = ⅓ × 12 × 8 = 32 units³
Slant Height ≈ 8.14 units (using Pythagorean theorem)
Lateral Area ≈ ½ × 16 × 8.14 ≈ 65.12 units²
Surface Area ≈ 12 + 65.12 ≈ 77.12 units²

About Triangular Pyramids

A triangular pyramid, or tetrahedron, is a three-dimensional shape with a triangular base and three triangular faces meeting at a common apex. It has 4 faces, 6 edges, and 4 vertices.

Real-World Applications

Chemistry: Molecular structures often form tetrahedral shapes
Architecture: Some roof designs use pyramid shapes
Gaming: 4-sided dice (d4) are triangular pyramids
Packaging: Some containers use pyramid shapes for stability

Types of Triangular Pyramids

Regular Tetrahedron: All faces are equilateral triangles
Right Triangular Pyramid: Apex is directly above the centroid of the base
Irregular Tetrahedron: Faces are different types of triangles

Triangular Pyramid Components

_Δ

Base Area (B)
B = ½ × b × h_Δ

Pyramid Height (h)

Lateral Area (L)
L = ½ × P × l

Surface Area (A)
A = B + L

Base Perimeter (P)
P = a + b + c

Volume (V)
V = ⅓ × B × h

How to Use the Triangular Pyramid Calculator

The Triangular Pyramid Calculator helps compute various properties based on input values. Here's how to use it:

1. Select Calculation Method

Choose what measurements you know:

Base Dimensions & Height - Enter triangle sides and pyramid height
Base Area & Height - When you know the base area
Volume & Base Area - To find the pyramid height
Surface Area - For regular tetrahedron calculations
Regular Tetrahedron - When all edges are equal

2. Enter Your Values

Input positive numbers in the appropriate fields:

Example 1: Base (b) = 6, Base Height = 4, Side a = 5, Side c = 5, Pyramid Height = 8

Example 2: Edge Length = 5 (for regular tetrahedron)

3. Get Results

The calculator will compute all properties:

Base Area (B)
Pyramid Height (h)
Volume (V)
Lateral Area (L)
Surface Area (A)
Base Perimeter (P)
Slant Height (l)

Practical Applications

Calculate material needed for pyramid-shaped structures
Determine paint required for tetrahedral objects
Find storage capacity of pyramid-shaped containers
Solve geometry problems involving triangular pyramids

Regular Tetrahedron Formulas

Parameter	Formula	Description
Edge Length (a)	Given	Length of any edge of the tetrahedron
Base Area (B)	(√3 / 4) × a²	Area of the equilateral triangular base
Height (h)	(√6 / 3) × a	Height from apex to base
Volume (V)	(a³) / (6√2)	Volume of the regular tetrahedron
Slant Height (l)	(√3 / 2) × a	Height of each equilateral face
Lateral Area (L)	3 × (√3 / 4) × a²	Sum of areas of the 3 lateral faces
Surface Area (A)	√3 × a²	Total surface area (4 faces)
Base Perimeter (P)	3 × a	Perimeter of the base triangle
Inradius (r)	(a × √6) / 12	Radius of sphere inscribed inside tetrahedron
Circumradius (R)	(a × √6) / 4	Radius of sphere circumscribing the tetrahedron

Frequently Asked Questions

1. What's the difference between a triangular pyramid and a triangular prism?

A triangular pyramid (tetrahedron) has one triangular base and three triangular faces meeting at an apex, while a triangular prism has two triangular bases and three rectangular faces.

2. How many faces does a triangular pyramid have?

A triangular pyramid has 4 triangular faces - one base and three lateral faces.

3. How do you find the height if you know volume and base area?

Use the formula: h = 3V / B where V is volume and B is base area.